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Update README for integer partition.

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Oleksii Trekhleb 2018-06-22 14:50:38 +03:00
parent 16b6ea506a
commit 831ce89a45
1 changed files with 11 additions and 14 deletions
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src/algorithms/math/integer-partition/integerPartition.js
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@ -34,20 +34,17 @@ export default function integerPartition(number) {
// any new ways of forming the number. Thus we may just copy the number from row above.
partitionMatrix[summandIndex][numberIndex] = partitionMatrix[summandIndex - 1][numberIndex];
} else {
// The number of combinations would equal to number of combinations of forming the same
// number but WITHOUT current summand number plus number of combinations of forming the
// <current number - current summand> number but WITH current summand.
// Example: number of ways to form number 4 using summands 1, 2 and 3 is the sum of
// {number of ways to form 4 with sums that begin with 1 +
// number of ways to form 4 with sums that begin with 2 and include 1} +
// {number of ways to form 4 with sums that begin with 3 and include 2 and 1}
// Taking these sums to proceed in descending order of intergers, this gives us:
// With 1: 1+1+1+1 -> 1 way
// With 2: 2+2, 2+1+1 -> 2 ways
// With 3: 3 + (4-3) <= convince yourself that number of ways to form 4 starting
// with 3 is == number of ways to form 4-3 where 4-3 == <current number-current summand>
// Helper: if there are n ways to get (4-3) then 4 can be represented as 3 + first way,
// 3 + second way, and so on until the 3 + nth way. So answer for 4 is: 1 + 2 + 1 = 4 ways
/*
* The number of combinations would equal to number of combinations of forming the same
* number but WITHOUT current summand number PLUS number of combinations of forming the
* <current number - current summand> number but WITH current summand.
*
* Example:
* Number of ways to form 5 using summands {0, 1, 2} would equal the SUM of:
* - number of ways to form 5 using summands {0, 1} (we've excluded summand 2)
* - number of ways to form 3 (because 5 - 2 = 3) using summands {0, 1, 2}
* (we've included summand 2)
*/
const combosWithoutSummand = partitionMatrix[summandIndex - 1][numberIndex];
const combosWithSummand = partitionMatrix[summandIndex][numberIndex - summandIndex];